Question

Planned expenditure function question with lump-sum tax

Do all parts to the question (show your work)

Assume in Fantasticland, MPC = 0.75, and autonomous consumption = $6000.  

Planned investment = $2000, and planned government purchases =  $5000. All Planned I and G are autonomous expenditures. Taxes ( T) is = $1000, and net exports = zero.

• a. Write out the consumption functionb.    

• What is induced consumption in this model?

• c.Write out the planned expenditure function (show your work)

• d.    Calculate current equilibrium real current GDP (income) (show your work)

• e.    How much is the expenditure multiplier?

• f.How much is the net tax multiplier

• g.At the current level of equilibrium, the economy is experiencing a recessionary gap $4000. How much is the full employment GDP?

• h.    How much will fantasticland change lump sum tax to close the recessionary gap?

• i.Write out the new planned expenditure function to reflect the change in lump sum taxes to close the recessionary gap of $4000.

• j.Graph the planned expenditure function. Show current equilibrium point, full employment Y, shift in planned expenditure for a change in lump-sum taxes. Label the autonomous points.
  

Answer 1

Answer:

(g) The Current level of Y can be determined as follows -

In Equilibrium, Y = C + I + G + NX

Y = C0 + cYd + I0 + G0 + NX

Or, Y = $6,000 + 0.75(Y - T0) + $2,000 + $5000 + 0

Or, Y = $13,000 + 0.75Y - 0.75*$1000 , (As T0 = $1,000)

Or, Y - 0.75Y = $13,000 - $750

Or, 0.25Y = $12,250

Or, Y = $12,250/0.25 = $49,000.

If in current Equilibrium i.e at Y = $49,000 the economy faces recessionary gap of $4,000.

Then full employment level of output or GDP of this economy is = $49,000 + $4,000 = $53,000. (Ans).

(h). The tax multiplier is = -MPC/(1 - MPC)

If MPC = 0.75, then net tax multiplier is = -0.75/(1 - 0.75) = -0.75/0.25 = -3.

As Net tax multiplier is = -3. The recessionary gap can be closed in following manner -

∆Y = (tax multiplier)∆T

Or, 4,000 = -3*∆T

Or, ∆T = -($4,000/3) = - $1,333.333

So, the change in Autonomous tax should be = - $1,333.33. It means the Autonomous tax should reduce by $1,333.333. The minus sign represent the direction of change and direction of change should be negative i.e it should be reduced.

(i). The planned expenditure function is -

AE = C + I + G + NX

In this planned expenditure function T will reduce by $1,333.333 i.e the new level of tax is = $1,000 - $1,333.33 = -$333.33.

The tax is = - $333.33. It should government subsidy. Because tax is negative and it implies there reverse payment from the government to public.

New planned expenditure function is

AE = C + I + G + NX

Or, AE = C0 + cYd + I0 + G0 + NX

Or, AE = $6,000 + 0.75(Y - T) + $2,000 + $5,000 + 0

Or, AE = $13,000 + 0.75Y - 0.75*(-$333.333)

Or, AE = $13,000 + 0.75Y + $249.999

Or, AE = $13,249.999 + 0.75Y

Or, AE = $13,250 + 0.75Y .....This is new AE function. (Ans)

The new equilibrium level of Y can be determined as follows

Y = AE in equilibrium

Or, Y = $13,250 + 0.75Y

Or, Y - 0.75Y = $13,250

Or, 0.25Y = $13,250

Or, Y = $13,250/0.25 = $53,000. (This is equivalent to full employment output. ). (Ans)

So, the change in tax = -$1333.333 is able to close the recessionary gap.

(j). Intial AE function is : AE = $12,250 + 0.75Y

New AE function is : AE = $13,250 + 0.75Y

We can plot the AE function , both initial and current.

X=AE AL AL PEo 45001 LOFOD 35.000 30,000 2000 20,000 15000 13,250 & 72,250 10.000 5000 o 10,000 10,000 65,000 50,000 30,000 40,000 49.000 53.000 (Real yop) E, : Current Equilibrium fprint .. Initin equilibrium point.